engleski

Identity Rule for Classical and Quantum Theories

It is shown that the identity rule---a rule of inference which has the form of modus ponens but with the operation of identity substituted for the operation of implication---turns any ortholattice into either an orthomodular lattice (a model of a quantum theory) or a distributive lattice (a model of classical theory). It is also shown that---as opposed to the implication algebras---one cannot construct an identity algebra although the identity rule contains the operation of identity as the only operation.

orthomodular lattices; distributive lattices; ortholattices; quantum logic; classical logic

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